For bonnet polishing of an aspheric surface, the tool influence function (TIF) is inevitably time varying, induced by the different surface curvatures on the aspheric surface. Accordingly, this paper investigated how the surface curvature affects the bonnet-workpiece contact area, and then presented a time-varying TIF model. The time-varying TIF was modeled based on the finite element analysis and kinematics analysis methods, and validated by experiments. The experimental results exhibited good agreement with the theoretical results. The proposed method can forecast the TIF for different polishing positions on aspheric surfaces, and provide the theoretical foundation for dynamic compensation of aspheric surface polishing.